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Generalized Learning Riemannian Space Quantization: A Case Study on Riemannian Manifold of SPD Matrices

IEEE Transactions on Neural Networks and Learning Systems, 2021
Learning vector quantization (LVQ) is a simple and efficient classification method, enjoying great popularity. However, in many classification scenarios, such as electroencephalogram (EEG) classification, the input features are represented by symmetric ...
Fengzhen Tang, Mengling Fan, Peter Tino   +2 more
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On a mapping in a riemannian space

Bulletin de la Classe des sciences, 1967
Srivastava Ramesh Chandra. On a mapping in a riemannian space. In: Bulletin de la Classe des sciences, tome 53, 1967. pp. 217-225.
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POLES OF PSEUDO-RIEMANNIAN SPACES

Mathematics of the USSR-Izvestiya, 1975
Two-dimensional complete analytic pseudo-Riemannian spaces with poles are studied. A pole is a point with respect to which admits a one-parameter group of rotations. With each pole is connected a holomorphic function (the complex pole function). Necessary conditions on are established.
Solodovnikov, A. S., Kamysanskii, N. R.
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Undulatory Riemannian Spaces

Journal of Mathematical Physics, 1963
A demonstration is given that Riemannian spaces of very high curvature in submicroscopic domains do not contradict the existence of a macroscopic line element which is nearly Minkowskian. The signature of the microscopic line element is positive definite and the wave property of the metric in macroscopic domains comes about by a peculiar ``wave-guide ...
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Multidimensional scaling in riemannian space

Journal of Mathematical Psychology, 1975
Abstract A metric which is a function of position is proposed for the analysis of the intrinsic geometry involved in preference or similarity judgments. Variation in the distance function or metric is characteristic of the Riemannian spaces and may be interpreted as curvature, stress or distortion in distance estimates and thus in the subjective ...
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Dirac matrices in riemannian space

Il Nuovo Cimento, 1958
An explicit formula is developed for the affine spinor connection, Γr, in an arbitrary spin representation. This formula makes it possible explicitly to write the Dirac equation in Riemannian space, γ i (Ψ, i -Λ i +mΨ=0, in a form which may be subjected to arbitrary similarity transformations.
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On generalized Riemannian spaces containing Riemannian subspaces

Russian Mathematics, 2007
In the paper, we establish conditions under which a generalized Riemannian space may contain a subspace with symmetric induced basic tensor. We consider the two cases. In the first case, a subspace is assumed to be given, and the problem is to find the skew-symmetric part of the basic tensor of the space.
S. M. Minčić, L. S. Velimirović
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Isometric immersions of Riemannian Spaces in Euclidean Spaces

Journal of Soviet Mathematics, 1980
Questions of the theory of isometric immersions of Riemannian spaces in Euclidean spaces beginning with the very first results onthis topic and also results on immersions of pseudo-Riemannian spaces in pseudo-Euclidean spaces and applications of the theory of immersions in the general theory of relativity are considered.
Poznyak, Eh. G., Sokolov, D. D.
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